virus?

In addition to removing malware with Malwarebytes, remove any Profile added by the adware.

   1. Remove unknown profiles if present.

      System Preferences > Profiles

      Open System Preferences, click the “Profiles” icon ( a checkmark on a gear) .

      When Profiles pane opens, select the unknown profile and click the minus button at the bottom.

  2. Remove unknown extensions:  Safari > Preferences > Extensions

      https://support.apple.com/guide/safari/use-safari-extensions-sfri32508/mac

Download and run Malwarebytes. Malwarebytes was developed by one of our own colleagues here in ASC and is about the most proven anti-malware software for Mac. It’s the only one recommended by Apple tech support folks.

Also check Safari/Preferences/General to see what your Home Page is set to. If Searchpulse, change it.

Safari Homepage setting greyed out